CN112935415A - Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method - Google Patents
Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method Download PDFInfo
- Publication number
- CN112935415A CN112935415A CN202110291776.3A CN202110291776A CN112935415A CN 112935415 A CN112935415 A CN 112935415A CN 202110291776 A CN202110291776 A CN 202110291776A CN 112935415 A CN112935415 A CN 112935415A
- Authority
- CN
- China
- Prior art keywords
- tooth
- variable
- thickness
- helical gear
- involute helical
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/20—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F21/00—Tools specially adapted for use in machines for manufacturing gear teeth
- B23F21/12—Milling tools
- B23F21/16—Hobs
Landscapes
- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Gears, Cams (AREA)
Abstract
The invention provides a variable tooth thickness involute helical gear hobbing and hobbing cutter design method, which comprises the steps that an equivalent conjugate relation is formed between every two of a variable tooth thickness involute helical gear hobbing cutter, a variable lead variable tooth thickness medium rack and a variable tooth thickness involute helical gear; calculating to obtain a tooth surface equation of the variable-lead and variable-tooth-thickness medium rack; calculating to obtain a tooth surface equation of the variable tooth thickness involute helical gear hob; manufacturing the variable tooth thickness involute helical gear hob according to the calculated tooth surface equation of the variable tooth thickness involute helical gear hob; the invention can finish the quick hobbing of the variable-tooth-thickness involute helical gear with the same modulus, the same pressure angle and different helix angles, is simple in design and convenient to manufacture corresponding to the gear hob, and provides a foundation for the batch production of the variable-tooth-thickness involute helical gear.
Description
Technical Field
The invention relates to the field of gear and gear hob design and processing, in particular to a variable tooth thickness involute helical gear hob processing and hob design method.
Background
The cylinder gear with involute helical teeth and variable tooth thickness for table tennis is a wide range of cylinder gears with involute helical teeth. The main geometrical characteristics are that the modification coefficient of each end face along the axial direction of the gear is changed linearly, and the helical angles at two sides are also different, so that a conical tooth top and a tooth root are formed, and the tooth thickness is changed linearly along the axial direction of the gear. The variable tooth thickness involute helical gear can transmit any type of rotary motion, including parallel shaft, intersecting shaft and staggered shaft rotary motion. And the precision transmission without backlash can be realized by controlling the relative axial position of the gear pair. At present, the variable tooth thickness involute helical gear is widely applied to the fields of full-drive automobile speed change systems, marine gear boxes, RV reducers for robots and other precise transmissions.
When the variable tooth thickness involute helical gear hob is used for processing, the hob is equivalent to a helical gear with unequal helix angles on two sides of a tooth surface and a larger helix angle, the tooth number of the hob is the number of heads of the hob, a workpiece is equivalent to another helical gear, the hob rotates at a fixed speed ratio, and the hob cuts a gear by a generating method according to the meshing principle of a helical gear pair.
Common gear manufacturing processes include gear milling, gear hobbing, gear shaping, gear shaving, gear shaping, gear grinding and the like. Wherein the hobbing process is most widely applied. The gear hobbing machine is high in production efficiency, high in machining precision and good in adaptability, and gears with the same modulus and pressure angle can be machined by adopting the same hobbing cutter. However, in the conventional gear hobbing machine for processing the variable tooth thickness involute helical gear, a radial feed transmission chain of a workpiece workbench relative to a tool rest is required to be added on the gear hobbing machine, and because the helical angles at two sides of the variable tooth thickness involute helical gear are different, the common hob needs to process tooth surfaces at two sides respectively. With the development of science and technology and the promotion of demand, the demand of variable tooth thickness involute helical tooth cylindrical gear is bigger and bigger, consequently needs higher machining efficiency.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a hobbing and hobbing cutter design method for a variable-tooth-thickness involute helical gear, so as to solve the problems in the technical background.
The purpose of the invention is realized by the following technical scheme:
a variable tooth thickness involute helical gear hobbing and hobbing cutter design method comprises the following steps:
s1, adding a variable-lead variable-tooth-thickness medium rack with variable lead and variable tooth thickness between conjugate tooth profiles of the variable-tooth-thickness involute variable-tooth-thickness gear hob and the involute variable-tooth-thickness gear, so that an equivalent conjugate relation is formed between every two of the variable-lead variable-tooth-thickness involute helical gear hob, the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear;
s2, calculating a tooth surface equation of the variable-lead variable-tooth-thickness medium rack according to the meshing function and the tooth surface parameters between the variable-tooth-thickness involute helical tooth cylindrical gears;
s3, calculating the tooth surface equation of the variable tooth thickness involute helical tooth cylindrical gear hob according to the tooth surface equation of the variable lead and variable tooth thickness medium rack;
s4, manufacturing the variable tooth thickness involute helical gear hob through the known calculated tooth surface equation of the variable tooth thickness involute helical gear hob;
s5, generating an involute tooth profile through the rotation of the variable-tooth-thickness involute helical gear hob and the generating motion of the rotation of the variable-tooth-thickness involute helical gear, and generating unequal helix angles on two sides through the combination of the axial movement of the variable-tooth-thickness involute helical gear hob and the axial movement along the processed gear, thereby completing the hobbing processing of the whole variable-tooth-thickness involute helical gear.
In the above summary, further, in step S1, a variable tooth thickness involute helical tooth cylindrical gear fixed coordinate system σ is constructednVarying tooth thicknessInvolute helical gear movable coordinate system sigma2And obtaining a tooth surface equation according to the gear meshing principle:
tooth surface equation of left tooth surface of variable tooth thickness involute helical gear
Comprises the following steps:
the tooth surface equation of the right tooth surface of the variable tooth thickness involute helical tooth cylindrical gear is expressed as follows:
in the formula, rb3And rb4Representing the base radius beta of the tooth surfaces at two sides of the variable tooth thickness involute helical gearLAnd betaRRepresenting the helical angles, delta, of the tooth surfaces at two sides of the variable tooth thickness involute helical gearLAnd deltaRRepresenting the tooth thickness parameter, alpha, of the two side tooth surfaces on the base circle of the variable-tooth-thickness involute helical gearnIs the normal pressure angle, lambda, of the variable tooth thickness involute helical geargRepresenting a moving parameter theta of a point on the tooth surface of the variable-tooth-thickness involute helical gear along the tooth height directiongRepresenting the moving parameters of points on the tooth surface of the variable tooth thickness involute helical tooth cylindrical gear along the tooth direction;
the expression of the meshing function between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear under the correct meshing condition that two conjugate tooth surfaces are not embedded or separated is as follows:
Φ2(u v)＝cosβ(ω2v-ω2lsinαn-v3 cosαn+ω2bcosαn)
in the formula, u and v media rack tooth surface coordinate parameters; beta is the helical angle of the left or right tooth surface of the involute helical gear with variable tooth thickness and omega2Involute helical tooth with variable tooth thicknessAngular velocity of rotation of the cylindrical gear, l being the distance traveled by the intermediate rack, v3The moving speed of the medium rack is used, and b is the meshing distance from the medium rack to the variable tooth thickness involute helical gear transmission;
according to the function of the contact line between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear, the function is as follows:
in the formula (I), the compound is shown in the specification,
for varying tooth thickness involute helical gear rotation angle i12The transmission ratio of the variable tooth thickness involute helical gear and the variable tooth thickness involute helical gear cylindrical hob is provided.
In the above summary, further, in step S2, a moving coordinate system σ of the connected media shelves is constructed3Constructing an auxiliary coordinate system σ connected to the left tooth surface5Building an auxiliary coordinate system σ connected to the right tooth surface5′，βLAnd betaRFor changing lead and tooth thickness, the inclination angle of two sides of the medium rack is changed as betaL≠βRTaking different values of pLAnd pRRespectively is the lead at both sides of the medium rack with variable lead and variable tooth thickness, SLAnd SRRespectively, a tooth thickness parameter, alphatRAnd alphatLThe tooth surface equation of the variable-lead variable-tooth-thickness medium rack is calculated by combining a meshing function between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear and tooth surface parameters, wherein the tooth surface equation is as follows: the left tooth surface of the variable-lead variable-tooth-thickness medium rack is at sigma5Tooth surface equation and unit normal vector in (1):
the right tooth surface of the variable-lead variable-tooth-thickness medium rack is at sigma5Tooth surface equation and unit method in `Vector quantity:
wherein u isLAnd vLIs a coordinate parameter of the left flank of the medium rack, uRAnd vRCoordinate parameters of the right tooth surface of the medium rack are obtained;
the meshing function expression between the medium rack with variable lead and variable tooth thickness and the involute helical gear hob with variable tooth thickness under the correct meshing condition that two conjugate tooth surfaces are not embedded or separated is as follows:
in the formula, ω1The method is characterized in that the rotating angular speed of the variable tooth thickness involute helical gear hob is adopted, a is the center distance between the variable tooth thickness involute helical gear hob and a hob, and beta is the tooth surface helical angle of the left side or the right side of the variable tooth thickness involute helical gear hob;
the function of the contact line between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear hob obtained according to the method is as follows:
in the above summary, further, in step S3, a hob fixing coordinate system σ of the variable tooth thickness involute helical gear is constructed1Variable tooth thickness involute helical gear movable coordinate system sigmamThe variable tooth thickness involute helical gear hob is characterized in that helical angles on two sides of the variable tooth thickness involute helical gear hob are different, the tooth thickness of the hob is changed linearly along the axial direction, the tooth surface of the variable tooth thickness involute helical gear hob is an involute helical surface, and a tooth surface equation of the variable tooth thickness involute helical gear hob is calculated by combining coordinates and a meshing function of a variable lead variable tooth thickness medium rack:
variable tooth thickness involute helical gear hob left sideTooth surface equation of tooth surface
Comprises the following steps:
the tooth surface equation of the right tooth surface of the variable tooth thickness involute helical gear hob is as follows:
in the formula, rb1And rb2Respectively is the base radius of the tooth surfaces at two sides of the variable tooth thickness involute helical gear hob, lambdawRepresenting the moving parameter theta of a point on the tooth surface of the variable tooth thickness involute helical gear hob along the tooth height directionwRepresents the moving parameter of a point on the tooth surface of the variable tooth thickness involute helical gear hob along the tooth direction, deltaLAnd deltaRRespectively is the tooth thickness parameter p of the base circle of the tooth surface at two sides of the variable tooth thickness involute helical gear hobLAnd pRThe lead of the tooth surfaces at two sides of the variable tooth thickness involute helical gear hob is respectively.
In the above invention, further, in step S5, the axial play v of the variable tooth thickness involute helical gear hob is2And axial movement v along the gear to be machined1The relationship of (1) is:
in the formula: alpha is alphanAt normal pressure angle, betaLAnd betaRFor varying lead and tooth thickness, pitch angle p on both sides of the medium rackLAnd pRThe lead is respectively arranged at two sides of the medium rack with variable lead and variable tooth thickness.
The variable tooth thickness involute helical gear and the hob thereof are characterized in that the tooth profiles, the modulus and the turning directions of the tooth surfaces on the two sides of the variable tooth thickness involute helical gear hob are the same, the lead angles are different, the variable tooth thickness involute variable tooth thickness hob forms gradually changed cutting edge thickness, the cutter tooth parts are distributed on a cutter body in a spiral manner, and the variable tooth thickness involute variable tooth thickness hob and the spiral angles of the tooth surfaces on the two sides of the variable tooth thickness involute helical gear respectively form a mutual complementary relationship.
In the above invention, each hob cutter tooth of the variable tooth thickness involute variable tooth thickness gear hob includes a front cutter face, a top edge rear cutter face, a side edge rear cutter face, a top edge and a cutting edge, and chip flutes are uniformly distributed between the cutter teeth.
The invention has the beneficial effects that: the variable-pitch variable-tooth-thickness medium rack is introduced to prove that the variable-tooth-thickness involute helical gear hob and the variable-tooth-thickness involute helical gear meet the involute gear meshing principle, so that the variable-tooth-thickness involute helical gear hob is designed and manufactured by establishing a tooth surface equation of the variable-tooth-thickness involute helical gear hob, and then the variable-tooth-thickness involute helical gear hob is processed by combining a generating method.
Drawings
FIG. 1 is a schematic view of a variable tooth thickness involute variable tooth thickness gear hob and a coordinate system thereof according to the present invention;
FIG. 2 is a schematic view of an involute spiral surface of a hob of a gear with variable tooth thickness and an involute tooth thickness;
FIG. 3 is a schematic view of a variable tooth thickness involute variable tooth thickness gear and its coordinate system of the present invention;
FIG. 4 is a schematic view of a variable tooth thickness involute variable tooth thickness gear processing coordinate system of the present invention;
FIG. 5 is a schematic view of a variable-lead and variable-tooth-thickness medium rack tooth surface according to the present invention;
FIG. 6 is a schematic view of the meshing relationship between the variable tooth thickness involute variable tooth thickness gear and the variable lead variable tooth thickness medium rack of the invention;
FIG. 7 is a schematic view of the meshing relationship between a variable tooth thickness involute variable tooth thickness gear hob and a variable lead variable tooth thickness medium rack according to the present invention;
fig. 8 is a schematic view of the meshing relationship between the medium rack i and the medium rack ii of the present invention:
FIG. 9 is a schematic view of the geometric relationship of the moving variable tooth thickness involute variable tooth thickness gear hob of the present invention;
FIG. 10 is a schematic view of the geometry of a moving variable tooth thickness involute variable tooth thickness gear of the present invention;
FIG. 11 is a schematic view of an instantaneous elliptical contact zone of the present invention;
FIG. 12 is a schematic view of the elliptical contact zone movement forming process surface of the present invention.
In the figure;
1-a variable tooth thickness involute helical gear hob;
2-a variable tooth thickness involute helical gear;
3-hob involute base circle;
4-hob involute helicoid;
5-involute of hob;
6-changing the tooth thickness involute helical gear left tooth surface base circle;
7-variable tooth thickness involute helical tooth cylindrical gear left tooth surface generating line;
8-variable tooth thickness involute helical tooth cylindrical gear left tooth surface;
9-changing the tooth thickness involute helical gear right flank;
10-changing the tooth thickness involute helical gear right tooth surface base circle;
11-medium rack right flank;
12-medium rack left flank;
13-a medium rack I;
14-rack and pinion right contact line;
15-contact line on left side of rack and pinion;
16-medium rack II;
17-hob rack right side contact line;
18-hob rack left contact line;
19-a media rack iv;
20-medium rack III.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
Example (b):
a variable tooth thickness involute helical gear hobbing and hobbing cutter design method comprises the following steps:
s1, adding a variable-lead variable-tooth-thickness medium rack with variable lead and variable tooth thickness between conjugate tooth profiles of the variable-tooth-thickness involute variable-tooth-thickness gear hob and the involute variable-tooth-thickness gear, so that an equivalent conjugate relation is formed between every two of the variable-lead variable-tooth-thickness involute helical gear hob, the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear;
s2, calculating a tooth surface equation of the variable-lead variable-tooth-thickness medium rack according to the meshing function and the tooth surface parameters between the variable-tooth-thickness involute helical tooth cylindrical gears;
s3, calculating the tooth surface equation of the variable tooth thickness involute helical tooth cylindrical gear hob according to the tooth surface equation of the variable lead and variable tooth thickness medium rack;
s4, manufacturing the variable tooth thickness involute helical gear hob through the known calculated tooth surface equation of the variable tooth thickness involute helical gear hob;
s5, generating an involute tooth profile through the rotation of the variable-tooth-thickness involute helical gear hob and the generating motion of the rotation of the variable-tooth-thickness involute helical gear, and generating unequal helix angles on two sides through the combination of the axial movement of the variable-tooth-thickness involute helical gear hob and the axial movement along the processed gear, thereby completing the hobbing processing of the whole variable-tooth-thickness involute helical gear.
The variable tooth thickness involute helical gear and hob are shown in attached body 1 and attached drawing 4, tooth profiles, modules and rotating directions of tooth surfaces on two sides of the variable tooth thickness involute helical gear hob 1 are the same, lead angles are different, the variable tooth thickness involute variable tooth thickness gear hob 1 forms a gradually changed cutting edge thickness, cutter tooth parts are distributed on a hob body in a spiral mode, and helix angles of the tooth surfaces on two sides of the variable tooth thickness involute variable tooth thickness gear hob 1 and the variable tooth thickness involute helical gear 2 respectively form a mutual complementary relationship.
Each hob cutter tooth of the variable tooth thickness involute variable tooth thickness gear hob 1 comprises a front cutter face, a top blade rear cutter face, a side blade rear cutter face, a top blade and a cutting edge, and chip flutes are uniformly distributed between the cutter teeth and the cutter teeth.
Referring to fig. 2, the variable tooth thickness involute helical gear hob 1 is essentially two involute helical surfaces with different helical angles, wherein one involute helical surface can be sigma1Describing that the tooth surface of the variable tooth thickness involute helical tooth cylindrical gear is an involute helical surface, the helical angles on two sides are unequal, and the formed tooth surface sigma is2As shown in fig. 3.
A variable-lead variable-thickness medium rack with variable lead and variable thickness is additionally arranged between the variable-tooth-thickness involute helical gear hob and the conjugate tooth surface of the variable-tooth-thickness involute helical gear. According to the novel meshing transmission analysis method with adjustable clearance, a coordinate system, sigma shown in figure 4 is establishedm(om-xm,ym,zm)，σn(on-xn,yn,zn) And σn(on-xn,yn,zn) Respectively are a fixed coordinate system corresponding to the variable tooth thickness involute helical gear hob 1, the variable tooth thickness involute helical gear 2 and the variable lead variable tooth thickness medium rack1(o1-x1,y1,z1)，σ2(o2-x2,y2,z2) And σ3(o3-x3,y3,z3) Respectively is a movable coordinate system omega connected with a variable tooth thickness involute helical gear hob, a variable tooth thickness involute helical gear and a variable lead variable tooth thickness medium rack1And ω2The angular velocities v of the variable tooth thickness involute helical gear hob and the variable tooth thickness involute helical gear3For variable lead and variable tooth thickness medium rack along zPThe linear velocity of the axial movement is,
and
the variable tooth thickness involute helical gear hob and the variable tooth thickness involute helical gear are respectively the rotating angles, and l is the moving displacement of the variable lead variable tooth thickness medium rack. The center distance between the hob and the gear is a, and the meshing distance of the rack transmission is b.
The variable-tooth-thickness involute helical gear hob is meshed with one side of the variable-lead variable-tooth-thickness medium rack on the left tooth surface of the variable-lead variable-tooth-thickness medium rack, and the variable-tooth-thickness involute helical gear hob is meshed with the other side of the variable-lead variable-tooth-thickness medium rack simultaneously. On the right tooth surface of the variable-lead variable-tooth-thickness medium rack, two sides of the variable-lead variable-tooth-thickness medium rack are respectively meshed with a variable-tooth-thickness involute helical gear hob and a variable-tooth-thickness involute helical gear. According to the Gamm's theorem, the variable tooth thickness involute helical gear hob and the variable tooth thickness involute helical gear must satisfy the conjugate relation after removing the variable lead and variable tooth thickness medium rack, namely the variable tooth thickness involute helical gear hob, the variable lead and variable tooth thickness medium rack and the variable tooth thickness involute helical gear have the equivalent conjugate relation. Therefore, by means of the variable-lead variable-tooth-thickness medium rack, the space meshing analysis of the variable-tooth-thickness involute helical gear hob and the variable-tooth-thickness involute helical gear is converted into the simpler meshing analysis of the variable-tooth-thickness involute helical gear rack and the variable-tooth-thickness involute helical gear hob rack.
The tooth surfaces of the variable lead and variable tooth thickness medium rack are shown in fig. 5, fig. 5(a) is the tooth surfaces and coordinate system of the variable lead and variable tooth thickness medium rack, and fig. 5(b) is the axial tooth profile. In the figure, σ3(o3-x3,y3,z3) Coordinate System moving coordinate System connecting media holders, same as in FIG. 4, σ5(o5-x5,y5,z5) The coordinate system is an auxiliary coordinate system connected to the left tooth surface, σ5′(o5′-x5′,y5′,z5') the coordinate system is the secondary coordinate system connected to the right flank. Beta is aLAnd betaRFor changing lead and tooth thickness, the inclination angle of two sides of the medium rack is changed as betaL≠βRTaking different values. p is a radical ofLAnd pRRespectively is the lead at both sides of the medium rack with variable lead and variable tooth thickness, SLAnd SRRespectively, a tooth thickness parameter, alphatRAnd alphatLThe two lateral pressure angles are respectively the variable lead and the variable tooth thickness medium rack.
According to the gear meshing principle, the parameters should satisfy the following conditions:
in the formula, mnIs a normal mode, αnThe normal pressure angle.
According to FIG. 5(a), the left tooth surface of the variable-lead and variable-tooth-thickness medium rack is at sigma5The tooth surface equation and unit normal vector in (1) can be expressed as
Wherein u isLAnd vLLeft flank parameters.
Also, at σ5In' the tooth surface equation and the right tooth surface unit normal vector can be expressed as:
wherein u isRAnd vRRight flank parameters.
According to the gear meshing principle, the meshing function of the left tooth surface of the variable-tooth-thickness involute helical tooth cylindrical gear hob and the variable-lead variable-tooth-thickness medium rack in the meshing process can be obtained in a coordinate system sigma through coordinate transformation and bottom vector conversion5The following expression is:
according to the gear meshing principle, the meshing function of the left tooth surface of the variable-tooth-thickness involute helical tooth cylindrical gear hob and the variable-lead variable-tooth-thickness medium rack in the meshing process can be obtained in a coordinate system sigma through coordinate transformation and bottom vector conversion5' the expression below is:
because the spiral angles at the two sides of the variable tooth thickness involute helical gear hob are different, the tooth thickness of the hob is changed linearly along the axial direction, and a coordinate system as shown in figure 1 is established. And the surface of the variable tooth thickness involute helical gear hob is an involute helical surface, and the tooth surface equation of the left tooth surface of the variable tooth thickness involute helical gear hob is shown in figure 2 by combining coordinate transformation differential geometry and a left tooth surface meshing function
Can be expressed as:
in the formula, rb1Is the base radius, lambda, of the left tooth surface of the cylindrical gear hob with the involute helical teeth and variable tooth thicknesswAnd thetawRespectively represents the tooth surface parameters, delta, of the variable tooth thickness involute helical gear hobLIs the tooth thickness parameter p of the base circle of the left tooth surface of the variable tooth thickness involute helical gear hobLThe lead of the left tooth surface of the variable tooth thickness involute helical gear hob is shown.
1) The left flank surface being around the axis Z of the hob1Rotation, angle of rotation ζ1Obtaining a new left tooth surface r of the positionL 2(λw,θw). The new left flank may be expressed as:
2) left flank along its axis Z1Moving in the direction to obtain a new left tooth surface r at the positionL 3(λw,θw). The new left flank may be expressed as:
comparing the different equations of motion of the left tooth surface twice, when h1＝pLζ1[ 2 ] and [ delta ]2＝δ1-ζ1Then, the following can be obtained:
rL 2(λw,θw)-rL 3(λw,θw)＝0
therefore, the geometric characteristic of the variable-tooth-thickness involute helical gear hob is that the tooth thickness of the variable-tooth-thickness involute helical gear hob gradually changes along the shaft, and the left tooth surface helical motion of the variable-tooth-thickness involute helical gear hob can be obtained to be equivalent to the translation motion along the shaft.
Based on the gear meshing principle, the left tooth surface and the variable-lead variable-tooth thickness of the involute helical gear can be obtained through coordinate transformation and bottom vector transformationCoordinate system sigma of meshing function in medium rack meshing process5The following expression is:
Φ2L(uL vL)＝cosβL(ω2vL-ω2lsinαn-v3 cosαn+ω2bcosαn)
according to the gear meshing principle, the meshing function of the left tooth surface of the involute helical tooth cylindrical gear with the variable tooth thickness and the variable lead in the meshing process of the variable tooth thickness medium rack can be obtained through coordinate transformation and bottom vector conversion5' the expression below is:
Φ2R(uR vR)＝cosβR(ω2vR-ω2lsinαn-v3cosαn+ω2bcosαn)
the tooth surface of the variable tooth thickness involute helical gear is an involute helical surface, and the helical angles are unequal on two side surfaces. Combining the coordinate-transformed differential geometry and the left flank meshing function may form a flank as shown in fig. 3. Tooth surface equation of left tooth surface of variable tooth thickness involute helical tooth cylindrical gear in graphic coordinate system
Comprises the following steps:
in the formula, rb3The radius of a base circle of the left tooth surface of the variable tooth thickness involute helical gear is as follows; alpha is alphanNormal pressure angle of the thick involute helical gear; lambda [ alpha ]gAnd thetagRespectively representing the tooth surface parameters of the variable tooth thickness involute helical gear; beta is aLRepresenting the left tooth surface helical angle of the variable tooth thickness involute helical gear; deltaLRepresenting the tooth thickness parameter of the left tooth surface on the base circle of the variable-tooth-thickness involute helical gear.
1) Axis Z of rotary left tooth surface winding variable tooth thickness involute helical tooth cylindrical gear2Make a spiral motion with an angleζ3To obtain a new left tooth surface of the position
The new left flank may be expressed as:
2) left flank along its axis Z2Moving in the direction of a displacement h3To obtain a new left tooth surface of the position
The new left flank may be expressed as:
comparing the different equations of motion of the left tooth surface twice, when h3＝rbζ3/3(cαonsβt,h3＝rb3ζ3/(cosαn tanβL) Then, the following can be obtained:
therefore, the variable tooth thickness involute helical gear has the geometrical characteristic that the tooth thickness of the variable tooth thickness involute helical gear is gradually changed along the shaft, and the left tooth surface helical motion of the variable tooth thickness involute helical gear can be equivalent to the translation motion along the shaft.
Similarly, in conjunction with the coordinate-transformed differential geometry and the right flank mesh function, the flank equation for the right flank can be expressed as:
in the formula, rb4Is a base circle half of the right tooth surface of the variable tooth thickness involute helical gearDiameter; beta is aRRepresenting the right tooth face helical angle of the variable tooth thickness involute helical gear; deltaRRepresenting the tooth thickness parameter of the right tooth surface on the base circle of the variable-tooth-thickness involute helical gear.
1) Right flank around its axis Z2Rotation, angle of rotation ζ4To obtain a new right tooth surface at the position
The new right flank can be expressed as:
2) right flank surface along its axis Z2Moving in the direction of a displacement h4To obtain a new right tooth surface at the position
The new right flank can be expressed as:
comparing the moving equations of the two different right tooth surfaces, when h is4＝rb4ζ4/(cosαn tanβR) And delta6＝δ5-ζ4Then, the following can be obtained:
therefore, the geometric characteristic of the variable-tooth-thickness involute helical gear is that the tooth thickness of the variable-tooth-thickness involute helical gear is gradually changed along the shaft, and the right-tooth-surface helical motion of the variable-tooth-thickness involute helical gear is equivalent to the translation motion along the shaft.
The spiral motion of the tooth surfaces at two sides of the variable tooth thickness involute helical gear hob and the variable tooth thickness involute helical gear is equivalent to the translation motion along the shaft, and the translation motion is integrated on the variable lead variable tooth thickness medium rack and the speed is consistent, so that the equivalent conjugate relationship is formed between every two of the variable tooth thickness involute helical gear hob, the variable lead variable tooth thickness medium rack and the involute variable tooth thickness involute helical gear.
The tooth surface equations of the whole variable-lead variable-tooth-thickness medium rack, the variable-tooth-thickness involute helical gear hob and the variable-tooth-thickness involute helical gear are established, the variable-lead variable-tooth-thickness medium rack is not attached to any entity and is formed by folding a piece of paper without thickness, one side of the variable-lead variable-tooth-thickness involute helical gear hob is meshed with the tooth surface of the variable-tooth-thickness involute helical gear hob, the other side of the variable-lead variable-tooth-thickness involute helical gear hob is meshed with the tooth surface of the involute variable-tooth-thickness involute helical gear, and the variable-lead variable-tooth-thickness involute. According to the Carm's theorem, after the variable-lead variable-tooth-thickness medium rack is drawn out, the variable-tooth-thickness involute helical gear hob and the involute variable-tooth-thickness involute helical gear inevitably meet the conjugate relation, namely the equivalent conjugate relation is formed between every two of the variable-tooth-thickness involute helical gear hob, the variable-lead variable-tooth-thickness medium rack and the involute variable-tooth-thickness involute helical gear.
According to the contact line variable equation, the variable tooth thickness involute helical gear and the variable lead variable thickness medium rack are meshed without backlash, as shown in figure 6. According to the contact line equation, the variable tooth thickness involute helical gear and the variable lead variable thickness medium rack are meshed without backlash, as shown in the attached figure 7. The position relationship between the medium rack I and the medium rack II is shown in figure 8, the right side surfaces of the medium rack I and the medium rack II are coplanar tooth surfaces, and the left side surfaces are standard gaps deltag. The medium rack I is meshed with the variable tooth thickness involute helical gear without backlash, and the medium rack II is meshed with the hob without backlash.
When the hob is along Z, as shown in FIG. 93Direction movement h1The variable-tooth-thickness involute helical gear is fixed, meanwhile, the medium rack II is moved to the medium rack IV, two tooth surfaces of the medium rack II are coplanar with the medium rack I, and the tooth gap variation delta of the variable-tooth-thickness involute helical geargAnd axial displacement h1Can be expressed as:
Δδg＝h1 cosαn|tanβL-tanβR|
as shown in FIG. 10, when the variable tooth thickness involute helical gear is along x3Direction movement h3The hob is fixed, the medium rack I moves to the medium rack III at the same time, two tooth surfaces of the medium rack I are coplanar with the medium rack II, and the tooth clearance variation delta of the variable tooth thickness involute helical geargAnd axial displacement h3Can be expressed as:
therefore, by utilizing the thickening characteristic of the medium rack, the variable-tooth-thickness involute helical gear is meshed with the hob without backlash, and the backlash deltagAnd also adjusted accordingly.
Axial play v of hob2And axial movement v along the gear to be machined1Can change the side clearance change delta of the involute helical gear through changing the tooth thicknessgAnd calculating the moving distance of the gear or the hob. Within the design processing time t, the hob needs to be along Z3Movement h1And in the gear axis direction x3Direction movement h3V can be obtained1And v2The calculation formula is as follows:
because the variable tooth thickness involute helical gear hob and the variable tooth thickness involute helical gear are moved, the tooth clearance variation deltagAre equal, so there are:
theoretically, the two conjugate tooth surfaces of the variable tooth thickness involute helical gear and the hob are in point contact, but after the tooth surfaces are deformed under load, an instantaneous elliptical contact area is formed in a tangent plane of the meshing point, as shown in the attached figure 11. As the hob rotates and moves axially along the gear, the contact zone moves along with it, thereby completing the generating machining of the gear surface, as shown in FIG. 12.
The above-mentioned embodiments only express the specific embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.
Claims (7)
1. A hobbing and cutting processing and hobbing cutter design method for a variable tooth thickness involute helical gear is characterized by comprising the following steps:
s1, adding a variable-lead variable-tooth-thickness medium rack with variable lead and variable tooth thickness between conjugate tooth profiles of the variable-tooth-thickness involute variable-tooth-thickness gear hob and the involute variable-tooth-thickness gear, so that an equivalent conjugate relation is formed between every two of the variable-lead variable-tooth-thickness involute helical gear hob, the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear;
s2, calculating a tooth surface equation of the variable-lead variable-tooth-thickness medium rack according to the meshing function and the tooth surface parameters between the variable-tooth-thickness involute helical tooth cylindrical gears;
s3, calculating the tooth surface equation of the variable tooth thickness involute helical tooth cylindrical gear hob according to the tooth surface equation of the variable lead and variable tooth thickness medium rack;
s4, manufacturing the variable tooth thickness involute helical gear hob through the known calculated tooth surface equation of the variable tooth thickness involute helical gear hob;
s5, generating an involute tooth profile through the rotation of the variable-tooth-thickness involute helical gear hob and the generating motion of the rotation of the variable-tooth-thickness involute helical gear, and generating unequal helix angles on two sides through the combination of the axial movement of the variable-tooth-thickness involute helical gear hob and the axial movement along the processed gear, thereby completing the hobbing processing of the whole variable-tooth-thickness involute helical gear.
2. The hobbing and hobbing method for cylindrical gears with varied tooth thickness involute and helical teeth as claimed in claim 1, wherein in step S1, a fixed coordinate system σ of cylindrical gears with varied tooth thickness involute and helical teeth is constructednVariable tooth thickness involute helical gear movable coordinate system sigma2And obtaining a tooth surface equation according to the gear meshing principle:
tooth surface equation of left tooth surface of variable tooth thickness involute helical gear
Comprises the following steps:
the tooth surface equation of the right tooth surface of the variable tooth thickness involute helical tooth cylindrical gear is expressed as follows:
in the formula, rb3And rb4Representing the base radius beta of the tooth surfaces at two sides of the variable tooth thickness involute helical gearLAnd betaRRepresenting the helical angles, delta, of the tooth surfaces at two sides of the variable tooth thickness involute helical gearLAnd deltaRRepresenting the tooth thickness parameter, alpha, of the two side tooth surfaces on the base circle of the variable-tooth-thickness involute helical gearnIs the normal pressure angle, lambda, of the variable tooth thickness involute helical geargRepresenting a moving parameter theta of a point on the tooth surface of the variable-tooth-thickness involute helical gear along the tooth height directiongRepresenting the moving parameters of points on the tooth surface of the variable tooth thickness involute helical tooth cylindrical gear along the tooth direction;
the expression of the meshing function between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear under the correct meshing condition that two conjugate tooth surfaces are not embedded or separated is as follows:
Φ2(u v)＝cosβ(ω2v-ω2lsinαn-v3cosαn+ω2bcosαn)
in the formula, u and v media rack tooth surface coordinate parameters; beta is the helical angle of the left or right tooth surface of the involute helical gear with variable tooth thickness and omega2The angular speed of rotation of the cylindrical gear with the involute helical teeth and variable tooth thickness is 1, the moving distance of the medium rack is v3The moving speed of the medium rack is used, and b is the meshing distance from the medium rack to the variable tooth thickness involute helical gear transmission;
according to the function of the contact line between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear, the function is as follows:
in the formula (I), the compound is shown in the specification,
for varying tooth thickness involute helical gear rotation angle i12The transmission ratio of the variable tooth thickness involute helical gear and the variable tooth thickness involute helical gear cylindrical hob is provided.
3. The method of claim 1, wherein in step S2, a movable coordinate system σ of the connecting medium frame is constructed3Constructing an auxiliary coordinate system σ connected to the left tooth surface5Building an auxiliary coordinate system σ connected to the right tooth surface5′，βLAnd betaRFor changing lead and tooth thickness, the inclination angle of two sides of the medium rack is changed as betaL≠βRTaking different values of pLAnd pRRespectively is the lead at both sides of the medium rack with variable lead and variable tooth thickness, SLAnd SRRespectively, a tooth thickness parameter, alphatRAnd alphatLThe tooth surface equation of the variable-lead variable-tooth-thickness medium rack is calculated by combining a meshing function between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear and tooth surface parameters, wherein the tooth surface equation is as follows:
the left tooth surface of the variable-lead variable-tooth-thickness medium rack is at sigma5Tooth surface equation and unit normal vector in (1):
the right tooth surface of the variable-lead variable-tooth-thickness medium rack is at sigma5Tooth surface equation and unit normal vector in':
wherein u isLAnd vLIs a coordinate parameter of the left flank of the medium rack, uRAnd vRCoordinate parameters of the right tooth surface of the medium rack are obtained;
the meshing function expression between the medium rack with variable lead and variable tooth thickness and the involute helical gear hob with variable tooth thickness under the correct meshing condition that two conjugate tooth surfaces are not embedded or separated is as follows:
in the formula, ω1The method is characterized in that the rotating angular speed of the variable tooth thickness involute helical gear hob is adopted, a is the center distance between the variable tooth thickness involute helical gear hob and a hob, and beta is the tooth surface helical angle of the left side or the right side of the variable tooth thickness involute helical gear hob;
the function of the contact line between the variable-lead variable-tooth-thickness medium rack and the variable-tooth-thickness involute helical gear hob obtained according to the method is as follows:
4. the hobbing method for machining and designing the hobbing cutter of the cylindrical gear with the involute and helical teeth with variable tooth thickness as claimed in claim 1, wherein in step S3, a hobbing cutter fixed coordinate system σ of the cylindrical gear with the involute and helical teeth with variable tooth thickness is constructed1Variable tooth thickness involute helical gear movable coordinate system sigmamThe variable tooth thickness involute helical gear hob is characterized in that helical angles on two sides of the variable tooth thickness involute helical gear hob are different, the tooth thickness of the hob is changed linearly along the axial direction, the tooth surface of the variable tooth thickness involute helical gear hob is an involute helical surface, and a tooth surface equation of the variable tooth thickness involute helical gear hob is calculated by combining coordinates and a meshing function of a variable lead variable tooth thickness medium rack:
tooth surface equation of left tooth surface of variable tooth thickness involute helical gear hob
Comprises the following steps:
the tooth surface equation of the right tooth surface of the variable tooth thickness involute helical gear hob is as follows:
in the formula, rb1And rb2Respectively is the base radius of the tooth surfaces at two sides of the variable tooth thickness involute helical gear hob, lambdawRepresenting the moving parameter theta of a point on the tooth surface of the variable tooth thickness involute helical gear hob along the tooth height directionwRepresents the moving parameter of a point on the tooth surface of the variable tooth thickness involute helical gear hob along the tooth direction, deltaLAnd deltaRRespectively, the tooth thickness is gradually changedTooth thickness parameter p of base circles of tooth surfaces on two sides of an open-line helical gear hobLAnd pRThe lead of the tooth surfaces at two sides of the variable tooth thickness involute helical gear hob is respectively.
5. The method as claimed in claim 1, wherein in step S5, the axial play v of the roller cutter is varied2And axial movement v along the gear to be machined1The relationship of (1) is:
in the formula: alpha is alphanAt normal pressure angle, betaLAnd betaRFor varying lead and tooth thickness, pitch angle p on both sides of the medium rackLAnd pRThe lead is respectively arranged at two sides of the medium rack with variable lead and variable tooth thickness.
6. The variable tooth thickness involute helical gear and the hob are characterized in that the tooth profiles, the modulus and the rotating direction of the tooth surfaces on the two sides of the variable tooth thickness involute helical gear hob are the same, the lead angles are different, the variable tooth thickness involute variable tooth thickness gear hob forms a gradually changed cutting edge thickness, the cutter tooth parts are spirally distributed on the cutter body, and the spiral angles of the tooth surfaces on the two sides of the variable tooth thickness involute helical gear hob and the variable tooth thickness involute helical gear respectively form a mutual complementary relationship.
7. The variable tooth thickness involute helical gear and hob according to claim 6, wherein each hob tooth of the variable tooth thickness involute helical gear hob includes a front cutter face, a top edge rear cutter face, a side edge rear cutter face, a top edge and a cutting edge, and flutes are uniformly distributed between the hob teeth and the hob teeth.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110291776.3A CN112935415B (en) | 2021-03-18 | 2021-03-18 | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110291776.3A CN112935415B (en) | 2021-03-18 | 2021-03-18 | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112935415A true CN112935415A (en) | 2021-06-11 |
| CN112935415B CN112935415B (en) | 2022-05-24 |
Family
ID=76228261
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110291776.3A Active CN112935415B (en) | 2021-03-18 | 2021-03-18 | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112935415B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113263225A (en) * | 2020-11-04 | 2021-08-17 | 北京航空航天大学 | Face gear honing shape-modifying method based on honing cutter pressure angle modification |
| CN114505543A (en) * | 2022-02-25 | 2022-05-17 | 重庆大学 | Involute surface enveloping ring surface worm tooth surface hobbing cutter confirming method based on medium gear |
Citations (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5481592A (en) * | 1977-12-12 | 1979-06-29 | Kobe Steel Ltd | Hob for processing screw-shaped rotor in screw compressor |
| JPS6052220A (en) * | 1983-09-02 | 1985-03-25 | Mitsubishi Heavy Ind Ltd | Semi-topping pinion cutter and its tooth profile grinding wheel |
| CN1049813A (en) * | 1990-07-04 | 1991-03-13 | 冶金工业部北京冶金设备研究所 | Novikov gear hob and do not have running-in amount gear |
| CN101028660A (en) * | 2007-04-06 | 2007-09-05 | 吉林大学 | Gear precisive hob configuration and its configured precisive hob |
| CN101526129A (en) * | 2009-02-27 | 2009-09-09 | 南京航空航天大学 | Helical involute gear and processing method thereof |
| CN102211234A (en) * | 2011-06-03 | 2011-10-12 | 南京航空航天大学 | Method for hobbing disc cylindrical gear type spiral involute gear |
| US20130089386A1 (en) * | 2011-10-07 | 2013-04-11 | Zhang-Hua Fong | Variable-Tooth-Thickness Worm-Type Tool and Method For Using The Same To Fabricate Gears |
| CN103100764A (en) * | 2013-02-09 | 2013-05-15 | 吉林大学 | Design method of 0-degree tooth profile angle helical tooth finish turning gear shaving cutter |
| CN203509232U (en) * | 2013-10-21 | 2014-04-02 | 合肥工业大学 | Pre-grinding hob for processing micro-segment gear |
| TW201617155A (en) * | 2014-11-06 | 2016-05-16 | Univ Feng Chia | Worm type cutter having dual-lead form and variable pressure angle, and operating method thereof |
| DE102016109307A1 (en) * | 2016-05-20 | 2017-11-23 | Robert Bosch Automotive Steering Gmbh | A rack measuring device, a rack-bending device, a method of determining a deviation of a rack, and a method of bending a rack |
| CN108856908A (en) * | 2018-07-06 | 2018-11-23 | 哈尔滨工业大学（威海） | The gear hobbing machine-tooled method and device of space beveloid gear pair |
| CN110434409A (en) * | 2019-07-26 | 2019-11-12 | 华南理工大学 | One kind parallels to the axis gear hob and its design method |
| CN111536218A (en) * | 2020-05-15 | 2020-08-14 | 重庆大学 | Point-line evolvable enveloping worm transmission pair and working mode thereof |
-
2021
- 2021-03-18 CN CN202110291776.3A patent/CN112935415B/en active Active
Patent Citations (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS5481592A (en) * | 1977-12-12 | 1979-06-29 | Kobe Steel Ltd | Hob for processing screw-shaped rotor in screw compressor |
| JPS6052220A (en) * | 1983-09-02 | 1985-03-25 | Mitsubishi Heavy Ind Ltd | Semi-topping pinion cutter and its tooth profile grinding wheel |
| CN1049813A (en) * | 1990-07-04 | 1991-03-13 | 冶金工业部北京冶金设备研究所 | Novikov gear hob and do not have running-in amount gear |
| CN101028660A (en) * | 2007-04-06 | 2007-09-05 | 吉林大学 | Gear precisive hob configuration and its configured precisive hob |
| CN101526129A (en) * | 2009-02-27 | 2009-09-09 | 南京航空航天大学 | Helical involute gear and processing method thereof |
| CN102211234A (en) * | 2011-06-03 | 2011-10-12 | 南京航空航天大学 | Method for hobbing disc cylindrical gear type spiral involute gear |
| US20130089386A1 (en) * | 2011-10-07 | 2013-04-11 | Zhang-Hua Fong | Variable-Tooth-Thickness Worm-Type Tool and Method For Using The Same To Fabricate Gears |
| CN103100764A (en) * | 2013-02-09 | 2013-05-15 | 吉林大学 | Design method of 0-degree tooth profile angle helical tooth finish turning gear shaving cutter |
| CN203509232U (en) * | 2013-10-21 | 2014-04-02 | 合肥工业大学 | Pre-grinding hob for processing micro-segment gear |
| TW201617155A (en) * | 2014-11-06 | 2016-05-16 | Univ Feng Chia | Worm type cutter having dual-lead form and variable pressure angle, and operating method thereof |
| DE102016109307A1 (en) * | 2016-05-20 | 2017-11-23 | Robert Bosch Automotive Steering Gmbh | A rack measuring device, a rack-bending device, a method of determining a deviation of a rack, and a method of bending a rack |
| CN108856908A (en) * | 2018-07-06 | 2018-11-23 | 哈尔滨工业大学（威海） | The gear hobbing machine-tooled method and device of space beveloid gear pair |
| CN110434409A (en) * | 2019-07-26 | 2019-11-12 | 华南理工大学 | One kind parallels to the axis gear hob and its design method |
| CN111536218A (en) * | 2020-05-15 | 2020-08-14 | 重庆大学 | Point-line evolvable enveloping worm transmission pair and working mode thereof |
Non-Patent Citations (2)
| Title |
|---|
| 李名扬: "可转位硬质合金滚刀设计及制造工艺的研究", 《中国优秀硕士学位论文全文数据库》 * |
| 相明君: "基于线接触共轭展成原理的齿轮精滚刀研究", 《中国优秀硕士学位论文全文数据库》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113263225A (en) * | 2020-11-04 | 2021-08-17 | 北京航空航天大学 | Face gear honing shape-modifying method based on honing cutter pressure angle modification |
| CN114505543A (en) * | 2022-02-25 | 2022-05-17 | 重庆大学 | Involute surface enveloping ring surface worm tooth surface hobbing cutter confirming method based on medium gear |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112935415B (en) | 2022-05-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN101526129B (en) | Helical involute gear and processing method thereof | |
| CN102725089B (en) | The continuation method of manufacture face gear | |
| CN109663991B (en) | Involute cylindrical gear enveloping milling method considering tooth surface precision characteristic | |
| CN112935415B (en) | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method | |
| CN104819266B (en) | Without escape arc spiral line mixed type herringbone bear and its processing method | |
| CN110131382B (en) | Non-backlash roller enveloping worm gearing mechanism | |
| CN102224360B (en) | Hypoid gears with low shaft angles | |
| CN108343725B (en) | Cycloidal gear tooth profile shaping method based on logarithm, cycloidal gear and RV reducer | |
| CN101774048A (en) | Bevel gear machining method | |
| CN114091210A (en) | Generating grinding tooth surface distortion prediction model construction method considering tooth profile modification | |
| CN101710350A (en) | Methods for designing and manufacturing double-lead linear contact bias worm drive | |
| CN112797119B (en) | Machining method of multi-head double-lead line contact offset worm | |
| CN102151911B (en) | Machining method for dual-lead linear contact offset worm drive | |
| CN112935420A (en) | Involute gear shaving cutter and three-dimensional modeling method and gear shaving processing method thereof | |
| CN112123038B (en) | Double-parameter single-side forming grinding method for rear cutter face of slotting cutter | |
| US20050063794A1 (en) | Method of producing an enveloping worm | |
| CN114769737A (en) | Forming and grinding processing method for gear with small number of teeth | |
| CN114505543B (en) | Involute surface enveloping ring surface worm tooth surface gear hobbing cutter confirmation method based on medium gear | |
| WO2004102036A2 (en) | Enveloping worm transmission and machining of enveloping worm transmission | |
| US6263571B1 (en) | Toothed gear design and manufacturing method | |
| CN101700587A (en) | Enveloping worm shaving method of hard tooth surface enveloping worm involute gear pair | |
| CN113927483B (en) | Face gear worm grinding wheel dressing method | |
| CN110280983B (en) | Method for machining face-tooth wheel vehicle teeth | |
| CN114309820A (en) | Gear single-side forming machining method combining customized cutter and specific path | |
| CN107617796A (en) | The process equipment of curved tooth line gear |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |